Introduction to the resistivity surveying method. The resistivity of ...

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function basically tells us the degree to which a change in the resistivity of a section of the
subsurface will influence the potential measured by the array. The higher the value of the
sensitivity function, the greater is the influence of the subsurface region on the measurement.
Note that for all the three arrays, the highest sensitivity values are found near the electrodes.
At larger distances from the electrodes, the contour patterns are different for the different
arrays. The difference in the contour pattern in the sensitivity function plot helps to explain
the response of the different arrays to different types of structures.
Table 2 gives the median depth of investigation for the different arrays. The median
depth of investigation gives an idea of the depth to which we can map with a particular array.
The median depth values are determined by integrating the sensitivity function with depth.
Please refer to the paper by Edwards (1977) listed in the Reference section for the details. In
layman's terms, the upper section of the earth above the "median depth of investigation" has
the same influence on the measured potential as the lower section. This tells us roughly how
deep we can see with an array. This depth does not depend on the measured apparent
resistivity or the resistivity of the homogeneous earth model. It should be noted that the
depths are strictly only valid for a homogeneous earth model, but they are probably good
enough for planning field surveys. If there are large resistivity contrasts near the surface, the
actual depth of investigation could be somewhat different. For example, it has been observed
that a large low resistivity body near the surface tends to create a “shadow zone” below it
where it is more difficult to accurately determine the resistivity values.
To determine the maximum depth mapped by a particular survey, multiply the
maximum “a” electrode spacing, or maximum array length “L“, by the appropriate depth
factor given in Table 2. For example, if the maximum electrode “a” spacing used by the
Wenner array is 100 metres (or maximum L 300 metres), then the maximum depth mapped is
about 51 metres. For the dipole-dipole, pole-dipole and Wenner-Schlumberger arrays, another
factor “n” must also be taken into consideration. For the arrays with four active electrodes
(such as the dipole-dipole, Wenner and Wenner-Schlumberger arrays), it is probably easier to
use the total array length “L”. As an example, if a dipole-dipole survey uses a maximum
value of 10 metres for “a” and a corresponding maximum value of 6 for n, then the maximum
“L” value is 80 metres. This gives a maximum depth of investigation of 80x0.216 or about 17
metres.
Table 2 also includes the geometric factor for the various arrays for an "a" spacing of
1.0 metre. The inverse of the geometric factor gives an indication of the voltage that would be
measured between the P1 and P2 potential electrodes. The ratio of this potential compared to
the Wenner alpha array is also given, for example a value of 0.01 means that the potential is
1% of the potential measured by the Wenner alpha array with the same "a" spacing.
2.5.1 Wenner array
This is a robust array that was popularized by the pioneering work carried by The
University of Birmingham research group (Griffiths and Turnbull 1985; Griffiths, Turnbull
and Olayinka 1990). Many of the early 2-D surveys were carried out with this array. In Figure
8a, the sensitivity plot for the Wenner array has almost horizontal contours beneath the centre
of the array. Because of this property, the Wenner array is relatively sensitive to vertical
changes in the subsurface resistivity below the centre of the array. However, it is less
sensitive to horizontal changes in the subsurface resistivity. In general, the Wenner is good in
resolving vertical changes (i.e. horizontal structures), but relatively poor in detecting
horizontal changes (i.e. narrow vertical structures). In Table 2, we see that for the Wenner
array, the median depth of investigation is approximately 0.5 times the “a” spacing used.
Compared to other arrays, the Wenner array has a moderate depth of investigation. The signal
Copyright (1999-2001) M.H.Loke